The major objective is to formulate mathematical and computational techniques and to apply them to problems of biomedical research and computer science. Research during FY85 was concentrated on Boolean algebras in a topos of sheaves on a locale. In particular, the notion of injectivity and related topics was studied and completed. A paper on this research has been accepted by the Mathematical Proceedings of the Cambridge Philosophical Society. Two more manuscripts on the study of Abelian groups in a topos of sheaves on a locale are complete except for some minor revisions. Development of computer software for faster and more flexible computer graphics was investigated in collaboration with LSM staff members. In addition, a study for the development of computer software for symbolic and algebraic calculations was begun.